Mathematics: A 25 gram sample of a substance that s used for drug research has a k-value of 0.1205. Find the substance s half life in days, round to the nearest tenth.

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A 25 gram sample of a substance that s used for

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blacee01

29.01.2022

Mathematics

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Situation: A 25 gram sample of a substance used for drug research has a k-value of 0.1205. N=N_0e^-kt

= initial mass(at time t=0) N= mass at a time t K= a positive constant that depends on the substance itself and on the units used to measure time T=time, in days

Find the substance's half-life in days, round to the nearest tenth.

5.8 days

Step-by-step explanation:

The decay model for drugs and radioactive substances is given as

$N=N_0e^{-Kt}$

The half-life of any substance is the time it takes for the substance to decay to half its initial amount. That is the period it takes for:

$N(t)=\dfrac{N_0}{2}$

If we substitute this into the model, we obtain:

$\dfrac{N_0}{2}=N_0e^{-Kt}\\$Dividing both sides by N_o\\\dfrac12=e^{-Kt}$

We can solve for t.

Taking the natural logarithm of both sides

$\ln\dfrac12=\ln e^{-Kt}\\\implies-\ln2=-Kt\\t=\dfrac{\ln2}{k} \\$Since k=0.1205$\\t_{1/2}=\dfrac{\ln2}{0.1205}=5.8$ days (to the nearest tenth)$

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A 25 gram sample of a substance that's used for drug research has a k-value of 0.1205. Find the substance's half life in days, round to the nearest tenth.

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